Mr. English would succeed John Key, who said on Monday he would step down

A ​54-year-old former farmer and one-time opposition leader is expected to become New Zealand’s next prime minister, after two challengers for the agriculture-rich nation’s top job​ conceded.

Bill English, the nation’s finance minister, emerged as the likely leader of the ruling center-right National Party on Thursday after two other candidates, Health Minister Jonathan Coleman and Corrections and Police Minister Judith Collins, said...